What are the odds of being dealt ace-king?
Preflop
Ace-king is dealt 1.21% of the time, or 1 in 82.9 hands; ace-king suited only 1 in 332.
- 1 in 110chance of ace-king offsuit
- 32.4%ace-king pairs at least one of its cards on the flop
- 48.7%the same by the river, all five cards seen
- 42.8%ace-king's equity all-in against queens
Frequency of the Hand
The lead states that ace-king appears in about one of eighty hands. This frequency includes both suited and offsuit combinations. The table below breaks down these specific distributions. Suited ace-king is less common than the offsuit version. Check the key figures to see the exact ratio for suited hands. The offsuit variant appears more frequently. These figures reflect the combinatorial possibilities of two distinct ranks. Since the suits are independent of rank selection, the suited combination requires matching suits, reducing its probability relative to the total set of ace-king hands. The offsuit hand allows for mismatched suits, increasing the number of possible combinations. This structural difference explains the disparity in frequency between the two variants.
| Starting hand | Chance per hand | Odds |
|---|---|---|
| Ace-king, any suits | 1.2% | 1 in 82.9 |
| Ace-king suited | 0.30% | 1 in 332 |
| Ace-king offsuit | 0.90% | 1 in 110 |
Pairing Probabilities
An unpaired hand such as ace-king pairs at least one card on the flop in about a third of deals. This chance is larger than the frequency of being dealt the hand itself. By the river, after all five board cards are seen, the likelihood of pairing at least one hole card rises to nearly half. The table above shows these progression steps. More board cards provide more opportunities to match a hole card rank. The increase from flop to river reflects the additional two cards revealed. This cumulative effect means that waiting for the river significantly improves the chance of hitting a pair compared to stopping at the flop. The probability depends on the number of unseen cards remaining in the deck.
Head-to-Head Equity
Against queens, ace-king holds an equity shown in the key figures when all-in before the flop. This figure is larger than the chance of pairing on the flop. It is also smaller than the probability of pairing by the river. The equity reflects the hand's strength relative to a high pocket pair. Queens start with a made pair, giving them an initial advantage. Ace-king relies on hitting an ace or king to overtake. The equity calculation assumes both players are all-in with no further decisions. This static comparison isolates the raw mathematical value of the hand combinations against each other without considering positional or strategic factors. If gambling stops being fun, free help is available at support resources.
Questions
Why is suited ace-king rarer than offsuit?
Suited hands require both cards to share the same suit. Offsuit hands allow any combination of suits. This constraint reduces the total number of possible suited combinations compared to offsuit ones.
Does pairing chance improve after the flop?
Yes. The chance to pair at least one hole card increases from the flop to the river. More board cards mean more opportunities to match a hole card rank.
How does ace-king fare against queens?
Ace-king has lower equity than queens when all-in before the flop. Queens start with a pair, while ace-king needs to hit an ace or king to win.
Where can I find help if gambling becomes difficult?
If gambling stops being fun, free help is available. Visit the support section for guidance on managing time and resources effectively.
Every figure on this page is computed by code from a standard 52-card deck, counting every possible card and checking the count a second way. See the methodology.